A community for students.
Here's the question you clicked on:
 0 viewing
mahela007
 4 years ago
Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session..
mahela007
 4 years ago
Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session..

This Question is Closed

ac7qz
 4 years ago
Best ResponseYou've already chosen the best response.0A "differentiable function" is one which is continuous over all the values of x you're interested in, and its derivative is also continuous. This means there are no sharp corners in the original function, only smooth transitions.

Tebello
 4 years ago
Best ResponseYou've already chosen the best response.1Differentiation is defined by a limit, and limits need not always exist. If the limit \[\lim_{h \rightarrow 0} \frac{f(x+h)  f(x)}{h}\] exists at a particular x value then we say the function is differentiable at that point. It it exists for all x in an interval then it is differentiable on that interval. Note that the limit is double sided, so implicit in this definition is the fact that no function defined on a closed interval can be differentiable on that closed interval, thus why the wording of many of the basic theorems insist on certain intervals being open...
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.